It's actually a lot more complicated than that. Her mother is Shia Muslim. Her father is Lebanese Druze. Druze are technically Muslim, but most other types of Muslim would say they are not. Right from Wikipedia:

Amal Clooney is fluent in English, French, and Arabic.[92][93] Her father is a Lebanese Druze[11][12][13][16][94] and her mother is a Lebanese Sunni Muslim.[16][17] Some reports have described Clooney as a Druze.[94] However, it is unlikely that she considers herself a part of the religion in any capacity, due to the Druze restriction on exogamy, her mother's Muslim faith, and her marriage to non-Druze George Clooney.[95][96] She has not publicly discussed her religion, but her husband said in an interview with The Hollywood Reporter that Amal Clooney is "nondenominational....not religious at all"

I would say she's more British than anything else, having lived there since she was 2. Oxford grad, and all. Marrying a non-Muslim is not something a Muslim girl of faith would do, and marrying a non-Druze is not something a Druze girl of faith would do.